管理科學(xué)與工程計(jì)算-作業(yè)題

1、科學(xué)與工程計(jì)算實(shí)驗(yàn)題V = _¥ _x _2第一題：（20）求解微分方程初值問題/。y（o）=i 自選方法，在步長h =0.05 , h2二0.05 2時(shí)求解，并與精確解y（x） = -1 - x 2e»進(jìn) 行比較；（2）在步長h和h2求解的基礎(chǔ)上，運(yùn)用外推方法提高求解精度。解：用改進(jìn)的Euler公式計(jì)算：令h=0.05結(jié)果如下：xyyrb01.0000e+0001.0000e+00005.0000e-0028.5250e-0018.5246e-0014.1151e-0051.0000e-0017.0975e-0017.0967e-0017.8289e-0051.5000e

2、-0015.7153e-0015.7142e-0011.1171e-0042.0000e-0014.3760e-0014.3746e-0011.4168e-0042.5000e-0013.0777e-0013.0760e-0011.6847e-0043.0000e-0011.8183e-0011.8164e-0011.9230e-0043.5000e-0015.9590e-0025.9376e-0022.1341e-0044.0000e-001-5.9128e-002-5.9360e-0022.3201e-0044.5000e-001-1.7450e-001-1.7474e-0012.4828

3、e-0045.0000e-001-2.8668e-001-2.8694e-0012.6242e-0045.5000e-001-3.9583e-001-3.9610e-0012.7458e-0046.0000e-001-5.0209e-001-5.0238e-0012.8494e-0046.5000e-001-6.0561e-001-6.0591e-0012.9363e-0047.0000e-001-7.0653e-001-7.0683e-0013.0080e-0047.5000e-001-8.0496e-001-8.0527e-0013.0657e-0048.0000e-001-9.0103e

4、-001-9.0134e-0013.1106e-0048.5000e-001-9.9486e-001-9.9517e-0013.1439e-0049.0000e-001-1.0865e+000-1.0869e+0003.1665e-0049.5000e-001-1.1762e+000-1.1765e+0003.1795e-0041.0000e+000-1.2639e+000-1.2642e+0003.1836e-004誤差小于3.18*10八-4 ；令h=0.025結(jié)果如下：xyyrb01.0000e+0001.0000e+00002.5000e-0029.2563e-0019.2562e-0

5、015.1759e-0065.0000e-0028.5247e-0018.5246e-0011.0096e-0057.5000e-0027.8050e-0017.8049e-0011.4771e-0051.0000e-0017.0969e-0017.0967e-0011.9208e-0051.2500e-0016.4002e-0016.3999e-0012.3417e-0051.5000e-0015.7144e-0015.7142e-0012.7407e-0051.7500e-0015.0395e-0015.0391e-0013.1185e-0052.0000e-0014.3750e-0014

6、.3746e-0013.4760e-0052.2500e-0013.7207e-0013.7203e-0013.8140e-0052.5000e-0013.0764e-0013.0760e-0014.1331e-0052.7500e-0012.4419e-0012.4414e-0014.4342e-0053.0000e-0011.8168e-0011.8164e-0014.7179e-0053.2500e-0011.2010e-0011.2005e-0014.9848e-0053.5000e-0015.9429e-0025.9376e-0025.2358e-0053.7500e-001-3.6

7、673e-004-4.2144e-0045.4712e-0054.0000e-001-5.9303e-002-5.9360e-0025.6919e-0054.2500e-001-1.1740e-001-1.1746e-0015.8983e-0054.5000e-001-1.7468e-001-1.7474e-0016.0911e-0054.7500e-001-2.3117e-001-2.3123e-0016.2708e-0055.0000e-001-2.8687e-001-2.8694e-0016.4378e-0055.2500e-001-3.4182e-001-3.4189e-0016.59

8、28e-0055.5000e-001-3.9603e-001-3.9610e-0016.7363e-0055.7500e-001-4.4952e-001-4.4959e-0016.8686e-0056.0000e-001-5.0231e-001-5.0238e-0016.9903e-0056.2500e-001-5.5441e-001-5.5448e-0017.1018e-0056.5000e-001-6.0584e-001-6.0591e-0017.2035e-0056.7500e-001-6.5661e-001-6.5669e-0017.2959e-0057.0000e-001-7.067

9、6e-001-7.0683e-0017.3793e-0057.2500e-001-7.5628e-001-7.5635e-0017.4541e-0057.5000e-001-8.0519e-001-8.0527e-0017.5208e-0057.7500e-001-8.5352e-001-8.5359e-0017.5796e-0058.0000e-001-9.0127e-001-9.0134e-0017.6310e-0058.2500e-001-9.4845e-001-9.4853e-0017.6751e-0058.5000e-001-9.9509e-001-9.9517e-0017.7125

10、e-0058.7500e-001-1.0412e+000-1.0413e+0007.7433e-0059.0000e-001-1.0868e+000-1.0869e+0007.7679e-0059.2500e-001-1.1319e+000-1.1319e+0007.7866e-0059.5000e-001-1.1764e+000-1.1765e+0007.7996e-0059.7500e-001-1.2205e+000-1.2206e+0007.8072e-0051.0000e+000-1.2642e+000-1.2642e+0007.8097e-005誤差小于7.8*10A-5 ;2、外推

11、一次：xyhyh/2wyrw-yr01.0000e+0001.0000e+0001.0000e+0001.0000e+00005.0000e-0028.5250e-0018.5247e-0018.5246e-0018.5246e-0011.1510e-0061.0000e-0017.0975e-0017.0969e-0017.0967e-0017.0967e-0014.8361e-0061.5000e-0015.7153e-0015.7144e-0015.7141e-0015.7142e-0015.9529e-0062.0000e-0014.3760e-0014.3750e-0014.3747

12、e-0014.3746e-0015.1605e-0062.5000e-0013.0777e-0013.0764e-0013.0760e-0013.0760e-0014.8995e-0063.0000e-0011.8183e-0011.8168e-0011.8163e-0011.8164e-0016.4414e-0063.5000e-0015.9590e-0025.9429e-0025.9375e-0025.9376e-0028.4610e-0074.0000e-001-5.9128e-002-5.9303e-002-5.9361e-002-5.9360e-0021.4254e-0064.500

13、0e-001-1.7450e-001-1.7468e-001-1.7474e-001-1.7474e-0013.6968e-0065.0000e-001-2.8668e-001-2.8687e-001-2.8693e-001-2.8694e-0015.3472e-0065.5000e-001-3.9583e-001 -3.9603e-001-3.9610e-001-3.9610e-0013.7126e-0066.0000e-001-5.0209e-001 -5.0231e-001-5.0238e-001-5.0238e-0016.6055e-0066.5000e-001-6.0561e-001

14、 -6.0584e-001-6.0592e-001-6.0591e-0018.2202e-0067.0000e-001-7.0653e-001 -7.0676e-001-7.0684e-001-7.0683e-0017.2742e-0067.5000e-001-8.0496e-001 -8.0519e-001-8.0527e-001-8.0527e-0012.2785e-0078.0000e-001-9.0103e-001 -9.0127e-001-9.0135e-001-9.0134e-0017.9282e-0068.5000e-001-9.9486e-001 -9.9509e-001-9.

15、9517e-001-9.9517e-0013.4694e-0069.0000e-001-1.0865e+000 -1.0868e+000 -1.0869e+000-1.0869e+0003.9319e-0059.5000e-001-1.1762e+000 -1.1764e+000-1.1765e+000-1.1765e+0005.1286e-0051.0000e+000-1.2639e+000 -1.2642e+000-1.2643e+000-1.2642e+0005.8882e-005誤差小于5.88*10八-5，但大部分誤差小于7.9*10A-6 ;第三題：（20分）價(jià)格、廣告與贏利某建材

16、公司有一大批水泥需要出售，根據(jù)以往的統(tǒng)計(jì)資料：零售價(jià)格高，則銷售量減少，具體數(shù)據(jù)現(xiàn)列于表1中；如果做廣告，可使銷售量增加具體增加量以銷售提高因子k表示,k與廣告費(fèi)的關(guān)系列于表 2中.現(xiàn)在已知水泥的進(jìn)價(jià)是每噸 250元問如何確定該批水泥的價(jià) 格和花多少廣告費(fèi)用，可使公司獲利最大？表1水泥預(yù)期銷售量與價(jià)格的關(guān)系單價(jià)（元ft）:250 260 270 280 290 300 310320銷量（104t） :200190176150139125110100表2銷售量提高因子與廣告費(fèi)的關(guān)系廣告費(fèi)（萬元）060120180240300360420提咼因子k :1.001.401.701.851.952.0

17、01.951.80提示:（1）可以用x，y，z，c分別表示單價(jià)、預(yù)期銷售量、廣告費(fèi)和成本單價(jià)，先根據(jù)表（1 ）和（2）用曲線擬合建立預(yù)期銷售量與單價(jià)及增量提高因子與廣告費(fèi)的關(guān)系（2）建立利潤函數(shù)的表達(dá)式利潤=銷售收入-成本-廣告費(fèi)用這里，實(shí)際銷售量=k 預(yù)期銷售量利用多元函數(shù)微分學(xué)求得問題的解解：1、列點(diǎn)圖分析：（1 ）、銷量與銷售單價(jià)的關(guān)系：設(shè)：銷量為x、銷售單價(jià)為y;4科學(xué)與工程計(jì)算實(shí)驗(yàn)題5科學(xué)與工程計(jì)算實(shí)驗(yàn)題-6.5768e-0013.8283e+002即：y=-0.65768*x+382.83(2)、銷售量提高因子與廣告費(fèi)的關(guān)系： 設(shè)銷量提高因子為 k、廣告費(fèi)用為乙#科學(xué)與工程計(jì)算實(shí)驗(yàn)

18、題顯示為拋物線，擬合曲線設(shè)為k= b2*zA2+b1*z+ b0結(jié)果顯示如下：p = -1.1822e-0056.8204e-0031.0188e+000即：k=-1.1822*10A-5*zA2+6.8204*10A-3*z+1.01882、利潤設(shè)為I,預(yù)期銷量為100（ 10A4t）即：x=100ky=-0.65768*x+382.83k=-1.1822*10A-5*zA2+6.8204*10A-3*z+1.0188c=250所以：l=y*x_z_c*x=(y-250)*x-z=(-65.768*k+382.83-250)*100*k-z=(-65.768*(-1.1822*10A-5*z

19、A2+6.8204*10A-3*z+1.0188 )+132.83)*100*(-1.1822*10A-5*zA2+6.8204*10A-3*z+1.0188)-z多項(xiàng)式計(jì)算：a仁0 -65.768;a2=-1.1822*10A-5 6.8204*10人-3 1.0188;p=c on v(a1,a2)P =7.7751e-004 -4.4856e-001 -6.7004e+001a仁0 07.7751e-004 -4.4856e-001 6.5826e+001;a2=-1.1822*10A-5 6.8204*10人-3 1.0188;p=c on v(a1,a2)P =0 -9.1917e-

20、0091.0606e-005 -3.0454e-003 -8.0333e-0036.7064e+001l=-9.1917*10A-7*zA4+1.0606*10A-3*zA3-3.0454 e-001*zA2-1.80333*z+6.7064e+003 編程：z=0:10:420;p=-9.1917e-0071.0606e-003 -3.0454e-001 -1.80333e-0006.7064e+003;l=polyval(p,z)plot(z,l,'*-r');ylabel('l 禾U潤');xlabel('z 費(fèi)用');結(jié)果顯示：l =5.

21、9817e+0032.3635e+0039.4785e+0001.0769e+0031.8979e+003Colu mns 1 through 116.7064e+0036.6590e+0036.5569e+0036.4061e+0036.2125e+0035.7190e+0035.4296e+0035.1185e+003 4.7902e+003 4.4494e+003Colu mns 12 through 224.1002e+0033.7467e+0033.3929e+0033.0421e+0032.6979e+0032.0417e+0031.7352e+0031.4467e+0031.1783e+0039.3209e+002Colu mns 23 through 337.0999e+0025.1357e+0023.4425e+0022.0318e+0029.1350e+001-4.1911e+001 -6.2521e+001 -5.2276e+001 -1.1320e+0015.9983e+001Co